Paper Keywords the practical application of abstract concepts in primary school mathematical models

Because school education has been influenced by "exam-oriented education" for a long time, students have strong knowledge and skills and poor practical application. Therefore, this paper introduces the concept of "mathematical model", and discusses how to help students establish mathematical models and the significance of establishing mathematical models, aiming at promoting students' interest in learning and improving their practical application ability. ?

First, the lack of application of mathematical models in mathematics teaching

One of the ideas of mathematics curriculum reform is that mathematics should strengthen its application consciousness and allow informationization. In fact, the application consciousness of mathematics in mathematics curriculum has long been common sense in developed countries, but the current application consciousness in China is very weak, which is incompatible with the development trend of mathematics curriculum in the world.

At present, most of the exercises in mathematics textbooks are pure mathematics problems divorced from the actual background, or applied mathematics problems with invisible background. Over time, such training makes students have strong ability to solve ready-made mathematical problems, but weak ability to solve practical problems. Teachers should be discerning, be good at transforming teaching materials, create operable and exploratory mathematical situations for students, guide students to explore the generation process of knowledge, and reproduce the life details of mathematical knowledge. Therefore, the concept of "mathematical model" is introduced.

Second, the concept definition

What is a mathematical model? Mathematical model can be described as: for a specific object in the real world, for a specific purpose, according to the unique internal laws, some necessary assumptions are simplified, and a mathematical structure is obtained by using appropriate mathematical tools. The process of establishing mathematical model is called mathematical modeling.

Third, the application of mathematical modeling in primary school mathematics

1, let students experience the process of forming mathematical concepts and explore mathematical laws. The overall goal of the new curriculum standard puts forward that students should "experience the process of abstracting some practical problems into problems of numbers and algebra, master the basic knowledge and skills of numbers and algebra, and solve simple problems." There must be a practical environment for students to experience. Students experience mathematics, understand mathematics and know mathematics through activities in the actual environment.

In teaching, "burning fish in pieces" often exists. There is not enough attention and training in the application of teaching, that is, there is no deliberate discussion and training on how to extract mathematical problems (fish head) from practical problems and how to apply mathematics to meet the special needs of practical problems (fish tail), and the practical background and application value of relevant mathematical concepts and theories are rarely revealed to students. In order to avoid this situation, teachers should help students to establish digital consciousness and explore different mathematical models at their own level. For example, when teaching continuous application problems, students can do simulated shopping. The clerk described how to settle the account and realized the difference between the two methods: Xiao Qiang brought 90 yuan money to buy a football 45 yuan and a volleyball 26 yuan. How much money should he get back? Most salespeople calculate this way: first subtract the money from a football from 90 yuan's money, and then subtract the money from a volleyball, and you get the money you want back. The formula is 90-45-26= 19 (yuan). A few salespeople have listed the formula: 45+26=7 1 (yuan) 90-7 1= 19 (yuan). I am sure of both methods, and the conclusion is that subtraction is always used to solve the residual problem. And summed up the mode of adding large numbers and subtracting decimals. Students only need to know whether they want large numbers or decimal numbers when doing problems, so as to cultivate students to observe and explain life from a mathematical point of view.

2. Set up math activity classes, attach importance to practical activities, and accumulate experience for students to solve problems. Offering math activity class allows students to use their brains and solve problems by themselves, which can help students get the background and situation of actual math problems, understand related terms and concepts, help students correctly understand the meaning of topics, and establish math models. It is a free world to cultivate students' initiative exploration spirit and practical ability.

For example, in the expansion class of "A few and which", a question appeared: from left to right, Xiaohua is the ninth, from right to left, Xiaohua is the eighth. How many people are there in this row? Before solving this problem, I asked a group of six people to stand up and count one of them, and found that it is directly 3+4=7, and there will be one more person. Why is this happening? After discussion, the students come to the conclusion that most of them have done it once, and we should subtract him. Then a model is obtained: the number from the left+the number from the right-1= the total number of people. With this model, it is much easier to solve such problems.

3. Guide students to solve problems with graphics and establish the transition from algebra to geometry. Algebra and geometry are not isolated. They also have something in common. We can use the concept of geometry to solve algebraic problems. Graphics is a more intuitive and effective form for junior students.

Example: Let students observe thermos, teacups, coke cans, telephone poles, trees, house pillars, etc. Through modern teaching methods (such as using CAI courseware or physical projector), learn to get rid of non-essential features such as handles, branches and colors. By analyzing the shapes of the main parts, with necessary assumptions, it is concluded that they have the same property: they can only roll in one direction, and the upper and lower bottom surfaces are round surfaces with the same size. In this way, by showing the above mathematical modeling process to students, students can know that mathematics comes from real life and there is mathematics everywhere in life. On this basis, students can be guided to apply mathematical knowledge to the reality of life and production. For another example, in the teaching of practical problems, we often use line graphs to solve them, effectively transforming text problems into graphics and making them easy to understand.

Fourth, the practical significance of mathematical model in primary school mathematics

1, through the study and discussion of mathematical modeling theory, it is beneficial to improve teachers' mathematical literacy. Generally speaking, in the process of modeling, we should keep the essential characteristics of the original problem and of course simplify it. This simplification is based on science, not entirely on mathematics. On the other hand, some simplification is necessary so that the obtained mathematical system is easy to handle. This requires teachers to have profound professional knowledge and help students build accurate mathematical models.

2. Establishing mathematical model can effectively stimulate students' thirst for knowledge. Mathematical model is a bridge between the basic knowledge of mathematics and its application. In the process of establishing and processing mathematical models, it is more important for students to realize the excellent opportunity to develop mathematics from reality, to obtain the re-creation of mathematics, and to make students more aware of the natural relationship between mathematics and nature and society. Therefore, in primary school mathematics teaching, it should be our knowledge to let students learn, do and use mathematics from realistic problem situations.

3. Mathematical modeling is an important way to cultivate students' modeling ability. Mathematical modeling is the whole process of finding the mathematical model of a specific problem, finding the solution of the model and verifying the solution of the model. Because primary school students mainly think in images, their mathematical models are related to the image map of Dachuan. Guide students to draw physical drawings, rectangular drawings and line drawings, and gradually establish mathematical models consciously and actively, and use them as excellent tools to solve problems, so as to enhance their interest and ability in this process.

Verb (abbreviation of verb) conclusion

The cultivation of students' modeling ideas is a long and complicated process, and the methods adopted are diverse and flexible. As long as teachers carefully design and patiently induce, all students can establish mathematical models of different levels.

References:

1, edited by Zhang Dianzhou, Introduction to Mathematics Education Research.

2. Chinese Mathematics Education for 2 1 century.

3. Hu Jiongtao's mathematics teaching theory

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